ON THE TOTAL INTENSITY OF INTERFERING LIGHT. 231 -limit of/™____2tt ^
cos "" (*'3 - «2 + y* - f) dx dy dx' dy'.
Now, when a vanishes, the whole of the integral
I.
-rf+f^-
is ultimately comprised between limits for which x' is infinitely close to x, and similarly with respect to y'; so that ultimately
cos-
\ab v "T* y'~x within the limits for which the quantity under the integral sign does not vanish. Hence, passing to the limit, we get
Z>2/ = X262 if das dy = \26l4, as before.
CASE III Everything the same as in Case II., except that the phase of vibration is retarded by p, where p is some function of x and y.
This case is very general. It includes, as particular cases, those numbered I. and II. The experiment with Fresnel's mirrors or a flat prism is also included as a particular case*.
From what precedes, it is plain that we should have in this case
Dtf-limitof"" 2a 2/?
{TT (a + b) r ,., 0 ,., ,n , , ) 7 7 7 , 7 , cos •{ [&>J— ^ + v 2 — y2]~- p -f p V aa? av M ay,
( \ab u }
* Thus, in the case of the flat prism, if P, Q be the virtual images corresponding to the halves AB, EG, if we produce AB to I), we may suppose the light which falls on BC, instead of coming from Q, to come from P, and to have been accelerated by the passage through the wedge DBG of air instead of the same wedge of glass,